Abstract
We study the gradient flow of the Riemannian functional ℱ(g):=∫M|Rm|2. This flow corresponds to a fourth-order degenerate parabolic equation for a Riemannian metric. We prove that the degeneracies may be accounted for entirely by diffeomorphism flow, and hence we show short-time existence using the DeTurck method. We prove L2 derivative estimates of Bernstein-Bando-Shi type and use these to give a basic obstruction to long time existence and prove a compactness theorem.
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